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Some Comments on Analysis Techniques for Censored Water Quality Data

In: Statistical Methods for the Assessment of Point Source Pollution

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  • V. T. Farewell

    (University of Waterloo, Department of Health Studies and Statistics and Actuarial Science)

Abstract

When investigating trace substances in ambient water, a proportion of water sample concentrations is usually below limits of detection. In medical and industrial reliability studies, comparisons are often made of time to event data which includes right censored observations indicating only that an observation is greater than a specified value. In this paper consideration is given to the application of non-parametric procedures, widely used in the analysis of time to event data, to water quality data which is left censored. A non-parametric estimate of the cumulative distribution function for left censored water quality data can be generated quite easily. For the comparison of levels of trace substances it is necessary to combine an unconditional likelihood for the proportion of observations below a detection limit with a partial likelihood for the portion of the distribution above the detection limit in order to make use of regression methodology. The details of this are outlined and an example is given which compares levels of toxic substances at the head and mouth of the Niagara river. When comparisons are based on matched pair data, further modifications are necessary. A development paralleling that for time to event data is given. Consideration is also given to model extensions which allow for a dependence between observations at the same location over a period of time. The presentation is introductory and designed to illustrate the potential of some available methodology for use in the analysis of water quality data.

Suggested Citation

  • V. T. Farewell, 1989. "Some Comments on Analysis Techniques for Censored Water Quality Data," Springer Books, in: D. T. Chapman & A. H. El-Shaarawi (ed.), Statistical Methods for the Assessment of Point Source Pollution, pages 185-193, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-1960-0_11
    DOI: 10.1007/978-94-009-1960-0_11
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